The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  1  2  2
 0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  0  0  8  0  0  0  0  8  8  0  8  8  8
 0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  0  8  8  8  0  8  0  8  0  0  0  8
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  0  8  0  8  8  0  8  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  0  8  8  8  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  8  8  0  0  8  0  0  0  0  8  0  8  8  8  0  8
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  8  8  8  0  0  8  0  8  0  8  8  0  8
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  0  0  8  8  0  8  8  8  8  8  8  8  0  0  8
 0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  0  0  8  8  0  8  8  8  0  0  8  0  0  0  8  0

generates a code of length 31 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+115x^24+28x^26+211x^28+140x^30+3072x^31+255x^32+84x^34+122x^36+4x^38+59x^40+3x^44+2x^48

The gray image is a code over GF(2) with n=248, k=12 and d=96.
This code was found by Heurico 1.16 in 5.17 seconds.